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Significant Figures and Scientific Notations. Examples and Problems. Rules for Counting Significant Figures. 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. Leading zeroes precede all the nonzero digits and DO NOT count as

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Significant Figures and Scientific Notations

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## Significant Figures and Scientific Notations

Examples and Problems

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

2. Zeros: There are three classes of zeroes.

• Leading zeroes precede all the nonzero digits and DO NOT count as

• significant figures. Example: 0.0025 has ____ significant figures.

• Captive zeroes are zeroes between nonzero numbers. These always

• count as significant figures. Example: 1.008 has ____ significant figures.

• Trailing zeroes are zeroes at the right end of the number.

• Trailing zeroes are only significant if the number contains a decimal point.

• Example: 1.00 x 102 has ____ significant figures.

• Trailing zeroes are not significant if the number does not contain a decimal

• point. Example: 100 has ____ significant figure.

• Exact numbers, which can arise from counting or definitions such as 1 in

• = 2.54 cm, never limit the number of significant figures in a calculation.

2

4

3

1

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination2006, page 53

### Significant figures: Rules for zeros

– three significant figures

0.421

Captive zeros are significant.

Captive zero

4012

– four significant figures

Trailing zeros are significant.

Trailing zero

114.20

– five significant figures

### Significant Figures

• Counting Sig Figs

• Count all numbers EXCEPT:

• Trailing zeros without a decimal point -- 2,500

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

3 SF

### Significant Figures

• Calculating with Sig Figs

• Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

4 SF

3 SF

324g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

### Significant Figures

• Calculating with Sig Figs (con’t)

• Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

224 g

+ 130 g

354 g

224 g

+ 130 g

354 g

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL

 350 g

 7.9 mL

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

### Significant Figures

• Calculating with Sig Figs (con’t)

• Exact Numbers do not limit the # of sig figs in the answer.

• Counting numbers: 12 students

• Exact conversions: 1 m = 100 cm

• “1” in any conversion: 1 in = 2.54 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

1. (15.30 g) ÷ (6.4 mL)

 2.4 g/mL

2 SF

### Significant Figures

Practice Problems

4 SF

2 SF

= 2.390625 g/mL

2. 18.9g

- 0.84 g

 18.1 g

18.06 g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

### Scientific Notation

65,000 kg  6.5 × 104 kg

• Converting into scientific notation:

• Move decimal until there’s 1 digit to its left. Places moved = exponent.

• Large # (>1)  positive exponentSmall # (<1)  negative exponent

• Only include sig. figs.

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

3. 2,400,000 g

4. 0.00256 kg

5. 7  10-5 km

6.6.2  104 mm

### Scientific Notation

Practice Problems

2.4  106 g

2.56  10-3 kg

0.00007 km

62,000 mm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

EXE

EXP

EXP

ENTER

EE

EE

### Scientific Notation

• Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44

7

8.1

4

÷

= 671.6049383

= 670 g/mol

= 6.7 × 102 g/mol

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem